Collisions between atomic and subatomic particles are oftenperfectly elastic. In one such collision, a proton traveling to theright at 258 km/s collides head-on and elastically with astationary alpha particle (a helium nucleus, having mass6.65x10^-27 kg). The electric potential energy function of theproton-alpha system when the separation is R is given by: Ue =(4.612x10^-28 /R) J/m. Atomic nuclei radii are approximately: R =A^1/3 (1.2x10^-12)m, where A is the total number of protons andneutrons in the nucleus. Considering only Ue and KE, how fast mustthe proton be moving directly toward the alpha nucleus for it tostop (without physical contact) at a stationary alpha's atomicradius? Under these conditions, the alpha nucleus may capture theproton, causing it to become a sodium nucleus. If this occurred,with what speed would the nucleus recoil? Assume (erroneously) thatmass is conserved in this interaction.
Note: All momentum analyses must begin with a FBD*, include anisolation test, and utilize the law of momentum conservation.
Collisions between atomic and subatomic particles are oftenperfectly elastic. In one such collision, a proton traveling to theright at 258 km/s collides head-on and elastically with astationary alpha particle (a helium nucleus, having mass6.65x10^-27 kg). The electric potential energy function of theproton-alpha system when the separation is R is given by: Ue =(4.612x10^-28 /R) J/m. Atomic nuclei radii are approximately: R =A^1/3 (1.2x10^-12)m, where A is the total number of protons andneutrons in the nucleus. Considering only Ue and KE, how fast mustthe proton be moving directly toward the alpha nucleus for it tostop (without physical contact) at a stationary alpha's atomicradius? Under these conditions, the alpha nucleus may capture theproton, causing it to become a sodium nucleus. If this occurred,with what speed would the nucleus recoil? Assume (erroneously) thatmass is conserved in this interaction.
Note: All momentum analyses must begin with a FBD*, include anisolation test, and utilize the law of momentum conservation.
